3:00 p.m., Friday (November 10, 2006)
Variational Methods in Riemannian Geometry
A fundamental question in Riemannian geometry is to understand the
relationships between the curvature and topology of Riemannian manifolds.
In classical Riemannian geometry, the second variation theory - in
particular index estimates - for geodesics plays a central role in results
of this nature, especially for studying manifolds with positive sectional
curvature. In more recent times minimal submanifolds, which require
hard analytic methods, have proven to have striking applications related
to the interconnection between the geometry and topology of manifolds.
In this talk we will discuss variational theory for volume with an
emphasis on minimal surfaces. We will give an overview of existence
results and the min-max construction of minimal surfaces in Riemannian
manifolds. We will also describe the work that has been done on stability
and Morse index for two dimensional surfaces and its applications,
especially to manifolds of positive isotropic curvature.
Refreshments will be served at 2:45 p.m. (Lounge, MATX 1115).